Talk by Sabine Bögli
On December 1st, 2021, Prof. Dr. Sabine Bögli (Durham University) gave a talk about "On the discrete eigenvalues of Schrödinger operators with complex potentials" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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In this talk I shall present constructions of Schrödinger operators with complex-valued potentials whose spectra exhibit interesting properties. One example shows that for sufficiently large $p$, namely $p>(d+1)/2$ where $d$ is the dimension, the discrete eigenvalues need not be bounded by the $L^p$ norm of the potential. This is a counterexample to the Laptev-Safronov conjecture (Comm. Math. Phys. 2009). Another construction proves optimality (in some sense) of generalisations of Lieb-Thirring inequalities to the non-selfadjoint case - thus giving us information about the accumulation rate of the discrete eigenvalues to the essential spectrum.
This talk is based on joint works with Jean-Claude Cuenin and Frantisek Stampach.
